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Lesson 2

# Lesson 2 - 5 4 lg 100 99 4 Determine x such that log x 2...

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Notation log a x = log a ( x ) ln x = log e ( x ) lg x = log 10 ( x ) lb x = log 2 ( x ) Note: If there is a problem written log x , assume that the base is not required to awnser the question (It will cancel out-Please check with me if it doesn’t). Rules for Logarithms log a ( xy ) = log a ( x ) + log a ( y ) log a x y = log a ( x ) - log a ( y ) log a ( x y ) = y log a ( x ) log a ( a x ) = a log a ( x ) = x log a (1) = 0 log a ( x ) = 1 log x ( a ) log a ( x ) log a ( y ) = log y ( x ) log a b ( x y ) = y b log a ( b ) WARNING: In log a b , both a AND b must be positive. Also log a (1) = 0 means that log 1 ( a ) is undefined and log 1 (1) is multi-valued.

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Problem Set 1. Solve for x : log (8) = x log (4) 2. Solve for x ( x > 1): log 3 ( x - 1) + log 3 ( x + 1) = 2 3. What is the sum of the following series? lg 2 1 + lg 3 2 + lg 4 3 + lg
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Unformatted text preview: 5 4 + ... + lg 100 99 4. Determine x such that log x 2 + log x 4 + log x 8 = 1. 5. What is the value of y in this equation? log 4 12 lb 4 + lb 4 lg 2 = lb y 6. How many digits are there in 2 1000 ? First lets ﬁnd the number of digits in 2 2 . 7. Find all values of x so that log 6 ( x + 3) + log 6 ( x-2) = 2 8. What is x if log 2 (27) + log 4 (9) + log 8 (3) = x log 2 3? 9. Solve for x in: lb x + 5 x-5 + lb ( x 2-25) = 0 10. What is-lb (lb ( p 4 √ 2)) + log 3 (log 3 ( 3 √ 3))?...
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Lesson 2 - 5 4 lg 100 99 4 Determine x such that log x 2...

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